Theorems · Theorem · commutative algebra
emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {N : Type u_2} [inst_2 : CommMonoidWithZero N]
[UniqueFactorizationMonoid N] [inst_4 : UniqueFactorizationMonoid M] {m p : Associates M} {n : Associates N}
(hp : p ∈ UniqueFactorizationMonoid.normalizedFactors m) (d : ↑(Set.Iic m) ≃o ↑(Set.Iic n)),
emultiplicity p m ≤ emultiplicity (↑(d ⟨p, ⋯⟩)) n- Defined in
- Mathlib.RingTheory.ChainOfDivisors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Unitsstatement · cited by 2,804
- Multisetstatement · cited by 2,627
- Set.Iicstatement and proof · cited by 1,111
- CommMonoidWithZerostatement and proof · cited by 913
- OrderIsostatement and proof · cited by 874
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- IsCancelMulZerostatement and proof · cited by 177
Cited by1
Results whose statement or proof uses this declaration.
- emultiplicity_prime_eq_emultiplicity_image_by_factor_orderIsoproof · cited by 1